this post was submitted on 30 Jun 2024
462 points (97.1% liked)

Science Memes

11130 readers
3335 users here now

Welcome to c/science_memes @ Mander.xyz!

A place for majestic STEMLORD peacocking, as well as memes about the realities of working in a lab.

Rules

  1. Don't throw mud. Behave like an intellectual and remember the human.
  2. Keep it rooted (on topic).
  3. No spam.
  4. Infographics welcome, get schooled.

This is a science community. We use the Dawkins definition of meme.

Research Committee

Other Mander Communities

Science and Research

Biology and Life Sciences

Physical Sciences

Humanities and Social Sciences

Practical and Applied Sciences

Memes

Miscellaneous

founded 2 years ago
MODERATORS
[email protected]
[email protected]
[email protected]
462
Dimensions (mander.xyz)
submitted 4 months ago by [email protected] to c/[email protected]
23 comments fedilink hide all child comments
 
you are viewing a single comment's thread
view the rest of the comments
[–] [email protected] 16 points 4 months ago* (last edited 4 months ago)

Fun fact, the Mandelbrot set is a 2-dimensional set (because it's defined in the complex plane). However, its boundary line is a fractal, which can be understood as having a non-integer dimension (i.e., between 1, the topological dimension of a line, and 2, the dimension of a plane). There are multiple ways to define fractal dimensions such as the Hausdorff dimension. For example, the Sierpinski triangle has a Hausdorff dimension of 1.58. But the Mandelbrot set is special here, too, as it seems to have a Hausdorff dimension of 2, meaning that its boundary is so curly that it fills "a plane's worth of space" despite its line-like topology.